Journal of Symbolic Logic 68 (4):1199-1241 (2003)

Cholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations
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DOI 10.2178/jsl/1067620182
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Degree Spectra of Intrinsically C.E. Relations.Denis R. Hirschfeldt - 2001 - Journal of Symbolic Logic 66 (2):441-469.

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